Four contributions to experimental economics [Elektronische Ressource] : binary choice experiments / vorgelegt von Thorsten Chmura

Four contributions to experimental economics [Elektronische Ressource] : binary choice experiments / vorgelegt von Thorsten Chmura

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Four Contributions to Experimental Economics: Binary  Choice  Experiments   Inaugural-Dissertation zur Erlangung des Grades eines Doktors der Wirtschafts- und Gesellschaftswissenschaften durch die Rechts- und Staatswissenschaftliche Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn vorgelegt von Dr. rer. nat. Diplom-Geologe Thorsten Chmura aus Memmingen Bonn 2010 Dekan: Prof. Dr. Christian Hillgruber Erstreferent: Prof. Dr. Dr. h. c. mult. Reinhard Selten Zweitreferent: Prof. Dr. Armin Falk Tag der mündlichen Prüfung: 08 September 2010 II Acknowledgment I am grateful to Reinhard Selten for his excellent support and his important advice, without his ideas and challenging discussions I would not work today in the field of behavioral economics. He is a great advisor and he was always helpful and shared his ideas. I like to thank Armin Falk for his valuable comments and his significant advice. Especially I like to Sebstian Goerg for his help and a great time in Bonn. I thank my office-roommates, friends and colleagues Sebastian Goerg, Johannes Kaiser and Thomas Pitz for sharing the office, the fruitful discussions, the adventurous evenings and a very pleasant time in Bonn.

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Four Contributions to Experimental Economics:
Binary  Choice  Experiments  



Inaugural-Dissertation


zur Erlangung des Grades eines Doktors
der Wirtschafts- und Gesellschaftswissenschaften


durch die


Rechts- und Staatswissenschaftliche Fakultät
der Rheinischen Friedrich-Wilhelms-Universität Bonn




vorgelegt von


Dr. rer. nat. Diplom-Geologe Thorsten Chmura

aus Memmingen




Bonn 2010















































Dekan: Prof. Dr. Christian Hillgruber
Erstreferent: Prof. Dr. Dr. h. c. mult. Reinhard Selten
Zweitreferent: Prof. Dr. Armin Falk



Tag der mündlichen Prüfung: 08 September 2010
II Acknowledgment


I am grateful to Reinhard Selten for his excellent support and his important advice, without
his ideas and challenging discussions I would not work today in the field of behavioral
economics. He is a great advisor and he was always helpful and shared his ideas.
I like to thank Armin Falk for his valuable comments and his significant advice. Especially
I like to Sebstian Goerg for his help and a great time in Bonn. I thank my office-
roommates, friends and colleagues Sebastian Goerg, Johannes Kaiser and Thomas Pitz for
sharing the office, the fruitful discussions, the adventurous evenings and a very pleasant
time in Bonn. I further like to thank my friends and colleagues: Sebastian Kube, Jan Meise,
and Gary Walkowitz for the evenings we spent, the work we did together and research
trips, which I always enjoyed.
For the financial support I like to say thank you to the Deutsche Forschungsgemeinschaft.
I appreciate and like to say thank you for the long friendship to Jens Wolf, Andreas
Schlechtriemen and Christoph Kremer.
Finally I wish to thank my family: Maja, Gerhard and Nadine, you have always been there
for me and gave me love and support. I like to thank Anna my mate and partner through the
years for her love, enduring patience and understanding.
III Executive Summary

This thesis is about binary decisions participants make in a laboratory environment. For this
purpose, laboratory experiments are conducted to investigate effects of individual decision
making in a microeconomic context. The first chapter is a short introduction and will give
an overview over the next four chapters In the second chapter comparisons between
theories in stationary 2x2 games and empirical data are investigated. Twelve 2x2 games
have been played in the laboratory and the results have been compared with 5 stationary
concepts. The third chapter reports experimental results on a simple coordination game in
which two players can coordinate either on an equal distribution of payoffs or on a Pareto
superior but unequal distribution of payoffs. The fourth chapter reports on simulations
applied on two similar congestion games: the first is the classical minority game. The
second one is an asymmetric variation of the minority game with linear payoff functions.
The fifth and last chapter reports results of laboratory experiments about traffic behavior of
participants with different cultural backgrounds. The minority game as an elementary
traffic scenario was chosen, in which human participants of a German and Chinese subject
pool had to choose over 100 periods between a road A and a road B.



IV Table of Contents

1.  Itroducntion   1  
2.  Stationary  Concepts  for  Experimental  2x2-­‐Games   3  
2.1.  Experimental  Liter ature  and  Introduction   3  
2.2.  The  Five  Stationary  Concepts   8  
2.2.1.  Equilibrium  Conditions  and  Their  Graphical  Rep   resentation 8  
2.2.2.  Nash  Equilibriu   m 11  
2.2.3.  Quantal  Response  Equilib   rium 11  
2.2.4.  Action-­‐sampling  Equilib  rium 13  
2.2.5.  Payoff-­‐sampling  Equilib  rium 14  
2.2.6.  Impulse  Balance  Equilib   rium 16  
2.3.  Experimental  Design   19  
2.3.1.  Procedu  re 19  
2.3.2.  Experimental  Ga   mes 20  
2.4.  Experimental  Results   24  
2.4.1.  Predicted  and  Observed  Relative  Frequ   encies 24  
2.4.2.  The  Measure  of  Predictive  Su   ccess 26  
2.4.3.  Comparison  of  Sample  Sizes  for  A -­‐samplinctiong  Equilib  rium 29  
2.4.4.  C ompample  Sizes  for  Pa -­‐samplinyoff g  Equilib  rium 30  
2.4.5.  Original  Versus  Transformed  Ga   mes 31  
2.4.6.  Comparison  of  the  Five  Theories   33  
2.4.7.  Changes  over  Ti me   34  
2.4.8.  Significance  of  the  Comparisons  of  Predictive  Su   ccess 35  
2.5.  Summary  and  Discussion   37  
3.   Testing  (Beliefs  about)  Social  Preferences:  Evidence  from  an  Expe tal  rimen
Coordination  Game   41  
3.1.  Introduction   41  
3.2.  Experimental  Seting  and  Design   42  
3.3.  Experimental  results   43  
4.  An  Extended  Rei orcement  Algorithm  for  Estimation  of  Human  Behaviour  in  
Experimental  Congestion  Games   48  
4.1.   The  Investigated  Games   48  
4.1.1.      Congestion  Game  I  (CI)    The  M –inority  Game   48  
4.1.2.     Asymmetric  Congestion  Game  s  (CII) 49  
4.1.3.     Experimental   -­‐up  Seotf  CI  and  CII 51  
4.2.     Reinforcement  Learning   51  
4.2.1.     Reinforcement  Algorithm  wi  Strath  Purtegiese   51  
4.2.2.     The  Empirical  Foundation  for  an  Extended  Reinforcem   ent  Model 52  
4.3.2.  Measuring  Direct  and  Contrarian  Stra   tegies 53  
4.2.4.       Extended  Reinforcnt  emeLearni  ng 53  
4.2.5.  Initial  Prop   ensity 54  
4.3.  Experimental  Statistics  and  Simulation  Results   57  
4.3.1.  CI  with  9  Pla   yers 57  
4.3.2.   CII  wth  18  Playeri   s 59  
4.3.3.   Simulations  of  CII  with  18,  36,  54,  72,    and  90  Players 60  
4.4.   Conclusion   61  
 
V
nf  
5.  Who  are  the  smarter  drivers?  The  Chinese  or  the  Germans?  An  Expmental  
Approach   63  
5.1.   Introduction   63  
5.2.   Experimental  setup   64  
5.3.   Experimental  results   66  
5.3.1.   Descriptive  statistics  fnes ore    the  Chiand  the  German  treatment   66  
5.3.2.   A  classifier  system  of  respo  nse  modes 68  
5.3.3.   Observed  Response  mode   69  
5.3.4.   Cumulative  Payoff   71  
5.4.   Conclusion   72  
Ref   73  
Appendi   78  
Appendix  2.A:  Table  of  Realative  Frequencies   78  
Appendix  2.B:  Written  instructions   80  
Appendix  2.C:  Screenshot  of  Game   81  
Appendix  2.D:  Monotonicity,  Existence  and  Uniqueness   82  
2.D1  Quantal  Response  Equilib   rium 82  
2.D2  A  property  of  the  binomial  distrib   ution 84  
2.D3  Action sa-­‐mpling  Equilib  rium 85  
2.D4  Payoff-­‐sampling  Equilib  rium 86  
2.D5  Impulse  Balance  Equilib   rium 88  
Appendix  2.E  Responsivenss  to  Own  Payoff  Parameters   88  
2.E1  Quantal  Response  Equilib   rium 89  
2.E2  Action -­‐sampling  Equilib  rium 89  
2.E3  Payoff-­‐sampling  Equilib  rium 89  
2.E4  Impulse  Balance  Equilib   rium 90  
Appendix  2.F:  A  Possibility  of  Generalizing  Impulse  Balance  Equilibrium   94  
Appendix  3.  Leaflet  to  Matrix  Experiment   95  
Appendix  4.  Graphical  Presentation  of  the  Statistical  Results   96  
Appendix  5.:  Who  are  the  Smarter  Drivers  Leaflet  and  Screenshot   99  
Appendix  5.A:    Leaflet  to  minority     experiment 99  
Appendix  5.B:  Screenshot  Of  The    Program 100  

















VI
x
enceser
ier
List of Figures

Figure  2.1:  Structure  of  the  experimental  2x2-­‐games.   8  
Figure  2.2:  The  cu rves  for   p  and  q  arising  in  the  example  of  game  1  for  each  of  the  five  con  cepts.10  U L
Figure  2.3:  Impulse  Balance  Transformation  for  the  example  of  experimental  game    3. 17  
Figure  2.4:  Impulse  in  the  direction  of  the  strategy  not  chose  n. 18  
Figure  2.5:  Experimentally  investigated  games.   21  
Figure  2.6:  Structure  of  the  pilot  experiments.   22  
Figure  2.7:  Permutations  of  rows,  columns,  or  player  roles  transform  the  6  experimental  games  into  44  
games  with  the  Nash  equilibria  shown  in  the  figure  . 23  
Figure  2.8:  Visualization  of  the  theoretical  equilibria  and  the  observed  average  in  the  con  su stma  n  t
games.   26  
Figure2.  9:  Overall  mean  squared  distancQes    for  the  action-­‐sampling  equilibria  with  different  sample  
sizes.   29  
Figure  2.10:  Overall  mean  squared  distanQce  fs  or  the  payoff-­‐samplingeq   uilibria  with  different  sample  
sizes.   31  
Figure  2.11:  Advantages  and  disadvantages  of  applying  a  concept  to  the  transformed  game  rather  the  
original  one.   32  
Figure  2.12:  Overall  mean  squared  distncesa  of  the  four  stationary  concepts  compared  to  the  observed  
average.   34  
Figure  2.13:  Comparison  of  predictive  success  in  the  first  half  and  second  half  of  the  expe  riments.35  
Figure  2.14:  Payoff  atrim x.   42  
Figure  3.15:  Choice  player  1  . 46  
Figure  3.16:  Choice  player  2  . 47  
Figure  4.17:  Participants  had  to  choose  between  a  road  [A]  and  a  road     [B]. 49  
Figure  4.18:  Reinforcement  algorithm   . 52  
Figure  4.19:  Initial  Propen  sities. 54  
Figure  4.20:  Number  of  players  on    A. 55  
Figure  4.21:  Standard  deviation  oumber  f  n of  players  on  A.   55  
Figure  4.22:  Number  of  changes  per  perio  d. 56  
Figure  4.23:  Mean  Yule-­‐coefficients.   56  
Figure  4.24:  Quadratic  deviations  of  the  best  initiators  l  vecfrom  the  average  experimental  data.   58  
Figure  4.25:  Example  simulation  shows  the  relative  payoff-­‐sum  for  each  of  the  9  players  over  
  1000  periods.   58  
Figure  4.26:  Distribution  of  the  mean  number  of  players  on    fBor  the  simulated  vector  (4,3,3,2)  in  1000  
simulations.   60  
Figure  5.27:  Number  of  participants  onA:    a  typical  session  of  the  German  and  the  Chinese  g  roup 67  
Figure  5.28:  Number  of  participants  on  road  A  for  the  German  and  the  Chinese  treatm   ent. 68  
Figure  5.29:  Mean  number  of  road  changes  for  the  German  and  the  Chinese  treatme  nt. 70  
Figure  5.30:  Yule-­‐Coefficient  for  the  German  and  the  Chinese  treatment.   70  
Figure  5.31:  Mean  cumulative  payoff  for  the  German  and  the  Chinese  treatment.   71  
Figure  5.32:  Spearmen  rank  correlation  coefficient  for  the  cumulative  payoff  vs.  t  nheumber  of  road  
changes.   72  
Figure  2.A1.33:  Visualization  of  the  theoretical  equilibria  and  the  observed  average  in  -­‐conthe  stannont  
sum  games.   79  
Figure  2.B1.34:  Schematics  of  game-­‐matrix.   80  
Figure  2.C1.35:  Screenshot  of  the  RatImage  Program  . 81  
Figure  A4.36:  Mean  Number  of  Players  on  B  in  Experiments  and  Simulatio  ns. 96  
Figure  A4.37:  Standard  Deviation  number  o  Pf layers  on  B  in  Experiments  and  Simulatio  ns. 96  
Figure  A4.38:  Number  of  Changes  in  Experiments  and  Simulations.   97  
Figure  A4.39:  Last  change  in  experiments  and  simulations.   97  
Figure  A4.40:  Mean  Yule-­‐coefficients  in  experiments  and  simulati  ons. 98  
Figure  A4.41:  Standard  Deviation  of  Y-­‐ulecoefficients  in  Experiments  and  Simulation   s. 98  
Figure  A5.42:  Screenshot  of  the  Program .   100  


VII
List of Tables

Table  1.  F1:ive  stationary  concepts  together  with  the  observed  relative  frequencies  for  each  of  the  
experimental  games.   24  
Table  2.2:  Squared  distances  of  the  five  theorie   s. 33  
Table  2.:  3 Significances  in  favor  of  row  concepts,  two  tailed  matched  pairs  Wilcoxon  signed  rank  test,  
rounded  to  the  next  higher  level  among   36  
Table  3.:4  Relativefreq   uency  of  decisions  (player    1). 44  
Table  3.  :5:  Relative  frequency  of  decisions  (playe  r  2). 44  
Table  3.:6  Resulting  distributio  ns. 45  
Table  4.7:  Pure  equilibria  I. in    ThCIe  equilibria  depend  on  the  number  of  participating  ag   ents. 50  
Table  4. :  C8 I–    9  Players    E-­‐xperimental  minima  &  maxima  vs.  simulation  means.   57  
Table  4. :  C9 I–I  1  8  Players    e-­‐xperimental  minima  &  maxima  vulation  means.   59  
Table  4.10:  CII  –Experimental  means  (E)  vs.  Simulation  means  (S)  . 61  
Table  5.11:  Statistical  data  of  the  experimen  ts. 66  
Table  5.12:x2    2table  for  the  computation  of  Yule-­‐coefficients.   68  
Table  A1.13:  Relative  frequencies  oUf  a  nd    inL  the  108  independent  subject  groups  for  games  1-­‐12.   78  






 
 
VIII CHAPTER 1: INTRODUCTION
1. Introduction
 
The  following  five  chapters  are  related  to  experimental  economics.  Every  chapter  
consists  out  of  an  already  published  or  submitted  paper.  
 
In the second chapter, entitled “Stationary Concepts for Experimental 2x2-Games” my
coauthor Reinhard Selten and I compare experimentally five stationary concepts for
completely mixed 2x2-games: Nash equilibrium, quantal response equilibrium, action-
sampling equilibrium, payoff-sampling equilibrium (Osborne and Rubinstein 1998) and
impulse balance equilibrium. Experiments on 12 games, 6 constant sum games and 6 non-
constant sum games are run with 12 independent subject groups for each constant sum
game and 6 independent subject groups for each non-constant sum game. Each independent
subject group consists of four players 1 and four players 2 interacting anonymously over
200 periods with random matching. The comparison of the five theories shows that the
order of performance from best to worst is as follows: impulse balance equilibrium, action-
sampling equilibrium, payoff-sampling equilibrium, quantal response equilibrium, Nash
equilibrium. The paper is accepted by the Journal American Economic Review and will be
published in 2008. Reinhar d  Selten  &  Thorsten  Chmura  )  (2008Stationary  Concepts  for  
Experimental  2x2  Games  will  appear008  i  Amern  Juican  ne  Economic  2 Review.   This  
paper  was  published  in  June  2008  in  the  American  economic  review.  At  the  beginning  
of   2009  Christoph   Brunner,   Colin   F.   Camerer   and   Jacob   K.   Goeree   submitted   a  
correction  of  this  paper  “A  correction   -­‐intand  erpretre atf  ion  ‘Stoationary  concepts  for  
experimental  2x2  games”  to  the  same  journal.  We  recalculated  their  corrections  and  
included  these  corrections  in  t   his  paper.

Chapter 3 of this thesis, entiteled „Testing (Beliefs about) Social Preferences: Evidence
from an Experimental Coordination Game” was written with the following coauthors
Sebastian Kube, Thomas Pitz and Clemens Puppe. This chapter reports experimental
results on a simple coordination game in which two players can coordinate either on an
equal distribution of payoffs or on a Pareto superior but unequal distribution of payoffs. We
find that the higher the difference in individual payoffs, the less likely is a successful
coordination on the Pareto superior distribution. While this is well in line with the recent
models of inequity aversion, our results are best explained not by a preference for equality
per se but rather by the belief that the opponent has such a preference. Thorsten  Chmura,  
Sebastian  Kube,  Thomas  Pitz  and  Clemens  Puppe  Testing  (2005)   (Belaboiefs  ut)  Social  
Preferences  :  Evidence  from  an  Experimental  Coordination    Economics  Letters,Game.  
Vol.  88  (2),  214-­‐220.
 
Chapter  4, “An Extended Reinforcement Algorithm for Estimation of Human Behavior in
Experimental Congestion Games” reports simulations applied on two similar congestion
games: the first is the classical minority game. The second one is an asymmetric variation
of the minority game with linear payoff functions. For each game, simulation results based
on an extended reinforcement algorithm are compared with real experimental statistics. It is
shown that the extension of the reinforcement model is essential for fitting the experimental
data and estimating the player's behavior. The paper was written with my coauthor Thomas
1 CHAPTER 1: INTRODUCTION
Pitz and published in the Journal of Artificial Societies and Social Simulations (JASSS) in
2007. Thorsten Chmura & Thomas Pitz (2007) Journal of Artificial Societies and Social
Simulation vol. 10, no. 2.
 
 
The last chapter entitled “Are the Chinese or the Germans the better Drivers?” reports
results of laboratory experiments about traffic behavior of participants with different
cultural backgrounds. This paper is written together with my coauthors Thomas Pitz and
Fei Fangyu. We conduct the minority game as an elementary traffic scenario in which
human participants of a German and Chinese subject pool had to choose over 100 periods
between a road A and a road B. In each period, the road that was chosen by the minority of
players win, these participants get a payoff. The payoff in the majority group is 0. An
important observation is that the number of road changes of a participant is negatively
correlated with his/her cumulative payoff. In this paper, particular emphasis shall be laid on
a comparison of the participants’ reaction to the immediately preceding payoffs. It could be
shown that Chinese participants reacted differently to the payoffs of preceding periods than
the German participants. The Chinese players did not change the route after bad payoffs as
often as the players of the German group. The Chinese comparison group is on average
able to attain better results because “bad” payoffs are more frequent in the minority game
than “good” ones. In the current draft the paper is a working paper. Thorsten Chmura,
Thomas Pitz, Fanyu Fei (2008): Who are the smarter Drivers? The Germans or the
Chinese? An Experimental Approach (submitted working paper).










 
 
 
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